The monthly rents (in dollars) paid by people are given below.

(Note that these are already ordered from least to greatest.)
880,910, 960,975,1000,1030,1070,1075
Suppose that one of the people moves. Her rent changes from 880 to 920.
Answer the following.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 days ago

To analyze the impact of the rent change from 880 to 920 on the group of monthly rents, let's first list the original monthly rents and then update them to reflect the change.

Original Rents:

  • 880
  • 910
  • 960
  • 975
  • 1000
  • 1030
  • 1070
  • 1075

Updated Rents (after the change):

  • 910
  • 920 (replacing 880)
  • 960
  • 975
  • 1000
  • 1030
  • 1070
  • 1075

Now let's answer some key statistical measures:

  1. Mean Rent:

    • Original Mean: \[ \text{Mean} = \frac{(880 + 910 + 960 + 975 + 1000 + 1030 + 1070 + 1075)}{8} = \frac{ 2, 820}{8} = 1027.5 \]

    • Updated Mean: \[ \text{Mean} = \frac{(910 + 920 + 960 + 975 + 1000 + 1030 + 1070 + 1075)}{8} = \frac{ 2, 100}{8} = 1050 \]

  2. Median Rent:

    • Original Median: Since there are 8 numbers, the median will be the average of the 4th and 5th numbers: \[ \text{Median} = \frac{(975 + 1000)}{2} = \frac{1975}{2} = 987.5 \]

    • Updated Median: The updated list still has 8 numbers, so the median remains: \[ \text{Median} = \frac{(960 + 975)}{2} = \frac{1935}{2} = 967.5 \]

  3. Mode Rent: There are no repeated rents in both cases, so:

    • Original Mode: None
    • Updated Mode: None
  4. Range of Rents:

    • Original Range: 1075 - 880 = 195
    • Updated Range: 1075 - 910 = 165

Summary of Results:

  • Original Mean: 1027.5
  • Updated Mean: 1050
  • Original Median: 987.5
  • Updated Median: 967.5
  • Original Mode: None
  • Updated Mode: None
  • Original Range: 195
  • Updated Range: 165

The changes in mean and median show how the changed rent impacts typical measurements of central tendency, and the range indicates that rents have become less spread out. If you have any specific statistical calculation you want to know or further analysis, please let me know!